Teslim süresi etkisi altında çok konumlu ürün çeşidi en iyilemesi

We have investigated the assortment planning problem for an online retailer that has multiple fulfilllment centers to maximize its expected profit. Each fulfilllment center is responsible for a customer segment which has its own customer profile, and each customer segment's demand is governed by a multinomial logit model (MNL), resulting in a mixtures of MNL (MMNL) model. A demand is primarily met by the responsible fulfilllment center, if available. However, if a product is not available in the responsible fulfilllment center, the demand can be met by fulfilllment centers in other regions at an additional shipping cost paid by the firm. The shipping cost depends on the distance between regions, so it varies by origin and destination. We assume that each customer has access to the entire assortment in all fulfilllment centers. To solve this problem, different from the literature, we have formulated the problem using a conic quadratic mixed integer programming approach. Later, the conic formulation is strengthened with valid inequalities. We have provided a numerical study to test the performance of our formulation against other formulations. Results show that our conic formulation together with the valid inequalities delivers outstanding performance compared to others in the literature. We also validated our approach using data from a local chain that operates in Northwestern part of Turkey.